The colors seen in a soap bubble or an oil film on water are a common example of interference. Light reflecting off the front and back surfaces of the thin soap film interferes, resulting in different colors being enhanced.
Constructive and destructive interference
Consider two waves that are in phase, sharing the same frequency and with amplitudes A1 and A2. Their troughs and peaks line up and the resultant wave will have amplitude A = A1 + A2. This is known as constructive interference.If the two waves are π radians, or 180°, out of phase, then one wave's crests will coincide with another waves' troughs and so will tend to cancel itself out. The resultant amplitude is A = |A1 − A2|. If A1 = A2, the resultant amplitude will be zero. This is known as total destructive interference.
When two sinusoidal waves superimpose, the resulting waveform depends on the frequency (or wavelength) amplitude and relative phase of the two waves. If the two waves have the same amplitude A and wavelength the resultant waveform will have an amplitude between 0 and 2A depending on whether the two waves are in phase or out of phase.
combined waveform | ||
wave 1 | ||
wave 2 | ||
Two sinusoidal waves in phase | Two sinusoidal waves 180° out of phase |
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